grotseis: Get seismic rotation matrix

In RSEIS: Seismic Time Series Analysis Tools

Get seismic rotation matrix

Description

Set up a rotation matrix for a seismic trace. Rotation matrix is 3D, although this rotation only creates a rotation for conversion to radial-transverse orientation.

Usage

grotseis(ang, flip = FALSE)

Arguments

ang	Angle to rotate horizontal components, degrees from North
flip	Logical, TRUE=flip the vertical axis, default=FALSE

Details

Returns a 3 by 3 matrix used for rotationg a 3-component seismic record, usually stored as an N by 3 matrix.

Only the N-E components are rotated, although the vertical component can be flipped.

It is important to note the order components are introduced in the rotation matrix. Here we assume East is X (to the right), and North is Y (to the top).

For data that has (V,N,E) as (1,2,3) need to switch components (1,3,2)

For data with (V,E,N) use the normal (1,2,3)

If Back-Azimuth is used, radial is directed towards the source. If azimuth is used, radial is directed away from the source.

Value

3 by 3 rotation matrix.

Note

Positive radial is away from the source (direction of wave propagation). Positive transverse is to the right when facing the direction of wave propagation.

Author(s)

Jonathan M. Lees<[e-mail]>

See Also

rdistaz

Examples

####  simple case:


vecs  <- rbind(c(0,0,1), c(0,1,0))
rbaz <- grotseis(21.76, flip=FALSE) 
bvec  <- vecs %*%  rbaz

plot(c(-2,2) , c(-2,2) , asp=1, xaxs="r"  , yaxs="r" , type='n' )

  arrows(0, 0, 0+bvec[,2], 0+bvec[,3],
     col=c("red", "blue"), length=.08)
     
  arrows(0, 0, vecs[,2], vecs[,3],
     col=c("red", "blue"), length=.08, lty=2)

text(0+bvec[1,2], 0+bvec[1,3], labels='radial', pos=3)
text(0+bvec[2,2], 0+bvec[2,3], labels='transverse', pos=4)

text(0+vecs[1,2], 0+vecs[1,3], labels='North', pos=3)
text(0+vecs[2,2], 0+vecs[2,3], labels='East', pos=4)

 
####  realistic case:
STAXY<-list()

STAXY$'x'<-c(-2.9162198461534,-2.49599248511068,
-2.85909405321704,-1.96135073099434,
-6.50413342506259,2.64026676599765,
-3.95701139503518,-2.84082134537436,
-0.0457817300378462,-2.74214190991955)
STAXY$'y'<-c(-7.83435541676815,-4.46180337254565,
-6.46036190991833,-5.01212763828746,
-2.56091416028758,
5.31173503708142,2.10545324503380,-0.87490923667824,
-0.172422188354707,-1.52055218789877)

STAXY$'lat'<-c(14.685621984127,14.7159182222222,
14.6979647030651,14.710975070028,
14.7329873333333,14.8037143111518
,14.7749104943935,14.7481391460905,
14.7544511215933,14.7423394025875)

STAXY$'lon'<-c(268.420918730159,268.424817925926,
268.421447725096,268.429783940243,268.387586722222,
268.472531954619,268.41123843527,268.421611351166,
268.447574716981,268.422528671994)

STAXY$'z'<-c(0.92522857142857,1.48225333333333,
1.14740517241379,1.4423781512605,1.51148,
2.53268681318681,2.70014678899083,2.04094444444444,
2.90827547169811,2.31817123287671)

STAXY$'cen'<-c(14.756,-91.552)

STAXY$name<-c('OBS','CAR','MAR','CAS','MTB','STA','STE','MOT','SUM','DOM')
sguitoXY<-list()
sguitoXY$'x'<-c(-1.78551922571555)
sguitoXY$'y'<-c(-1.80850340813817)
sguitoXY$'lat'<-c(14.7397535236)
sguitoXY$'lon'<-c(268.4314147874)
sguitoXY$'z'<-c(2.501)

DAZ <- rdistaz( sguitoXY$lat, sguitoXY$lon ,       STAXY$lat, STAXY$lon)

STAXY$az <- DAZ$baz

####  plotting
plot(STAXY$x, STAXY$y, asp=1, xaxs="r"  , yaxs="r" )
text(STAXY$x, STAXY$y,STAXY$name, pos=3)
points(0,0, pch=3)
points(sguitoXY$x,sguitoXY$y , pch=8)
segments(sguitoXY$x, sguitoXY$y, STAXY$x, STAXY$y, col="green", lty=2)

#### be aware of the convention used: (V-N-E) or (V-E-N)
### here first vector is east, second vector is north
###       if you use the V-N-E convention
vecs  <- rbind( c(0,1,0), c(0,0,1))

for( i in 1:length(STAXY$x))
  {
rbaz <- grotseis(STAXY$az[i], flip=FALSE)
bvec  <- vecs %*%  rbaz
##############   red is north, blue east
########         red is radial positive away or toward  source, blue is transverse
##########       blue is positive rotated to the right of red
##
arrows(STAXY$x[i],STAXY$y[i], STAXY$x[i]+bvec[,2], STAXY$y[i]+bvec[,3],
col=c("red", "blue"), length=.08)

}

RSEIS documentation built on Sept. 13, 2024, 1:09 a.m.